Problem: Simplify the following expression: $a = \dfrac{r^2 - 9r - 10}{r - 10} $
Explanation: First factor the polynomial in the numerator. $ r^2 - 9r - 10 = (r - 10)(r + 1) $ So we can rewrite the expression as: $a = \dfrac{(r - 10)(r + 1)}{r - 10} $ We can divide the numerator and denominator by $(r - 10)$ on condition that $r \neq 10$ Therefore $a = r + 1; r \neq 10$